A038564 Numbers whose list of divisors includes each digit 1-9 equally often.

54023, 54203, 55868, 500407, 556744, 769858, 1187666, 1566986, 1875098, 3545924, 5594156, 5733406, 5849014, 5908304, 6100594, 6712006, 7605544, 9106868, 9580654, 10909864, 23456789, 23458679, 23459687, 23465789, 23465987, 23469587, 23475869, 23478569, 23489657

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

55868 is a term because, among its divisors (which are 1, 2, 4, 13967, 27934, 55868), each digit from 1 through 9 occurs exactly twice.

Mathematica

ld9Q[n_]:=Module[{d=DeleteCases[Sort[Flatten[IntegerDigits/@Divisors[ n]]], 0]}, Length[ Intersection[ d, Range[ 9]]] == 9&&Length[Union[ Length/@Split[ d]]]==1]; Select[ Range[ 235*10^5], ld9Q] (* Harvey P. Dale, Dec 20 2022 *)

Prog

(Python)
from sympy import divisors
from collections import Counter
def ok(n):
    c = Counter()
    for d in divisors(n, generator=True): c.update(str(d))
    return len(set([c[i] for i in "123456789"])) == 1
print([k for k in range(1, 60000) if ok(k)]) # Michael S. Branicky, Nov 13 2022

Crossrefs

Cf. A038565.

Sequence in context: A151959 A164724 A190472 * A243362 A224624 A202467

Adjacent sequences: A038561 A038562 A038563 * A038565 A038566 A038567

Keyword

nonn,base,easy

Author

Naohiro Nomoto

Extensions

More terms from Sascha Kurz, Oct 18 2001

a(26) and beyond from Michael S. Branicky, Nov 13 2022

Status

approved